is a formula indicating that the items connected by it can be taken either together or as alternatives. Its principal uses are in legal and other formal documents (These ratios indicated that the changes in the order of crystallinity were similar to those with the water content and/or dehydration and temperature for gelatinization among and/

• or within cultivars —Annals of Botany, BrE 2001)

and in logic (The best philosophy…embodies a picture of the world and/

• or a set of values —E. Craig, 2002).

In general use the effect can be ungainly:

• Stalin, characteristically insensitive to Western public opinion and/or relying on the political ambiguity of these phrases in the existing context, signed it —Cambridge Review, 1959.

A more comfortable way of expressing the same idea is to use ‘X or Y or both’, and in some cases ‘or’ by itself will do.
1. When or separates two singular nouns, the following verb should be in the singular:

• A paint or steel company or a salt or coal mine was no place for the late Herr Baumgartner's widow —Anita Desai, 1988.

(When both nouns are plural the verb is of course also plural.) The following example is acceptable informally, but strictly or should be replaced by and, or the plural complement replaced by a singular one (…is a typical method):

• ☒ A cassette recorder or disk system are typical methods —Choosing and using Your Home Computer, 1984.

When one of the nouns is singular and the other plural, the verb normally agrees with the one nearer to it, and the same applies to mixes of person as in she or we, you or your brother, etc.: The child or its parents sign the form / Were you or your brother there?.
2. For or after either see either 2b, and after neither see neither 5.

Modern English usage. 2014.